Darcy-Weisbach Equation

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Darcy-Weisbach Equation, abbreviated as DW, a dimensionless number, is the most common way of expressing the pressure drop of a piped fluid.  The equation is valid for fully developed, steady state and incompressible flow. The Darcy-Weisbach equation with the Moody Diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow.

Darcy-Weisbach Equation FORMULA

(Eq. 1)  \(\large{ h_l = \frac   { f_d \;  l \;  v^2   }   { 2 \; d \; g   }   }\) 

(Eq. 2)  \(\large{ h_l = f_d \;  \frac{ l }{ d } \; \frac{ v^2}{ 2 \; g}   }\)        

Where:

\(\large{ h_l }\) = head loss

\(\large{ v }\) = mean flow velocity

\(\large{ f_d }\) = Darcy friction factor

\(\large{ g }\) = gravitational acceleration

\(\large{ d }\) = pipe inside diameter (ID)

\(\large{ l }\) = pipe length

Solve for:

\(\large{ v =   \sqrt {  \frac  { 2 \; h_l \;  d  \;  g   }   { f_d \; l   }        }   }\)

\(\large{ f_d = \frac   { 2 \; h_l  \;  d \; g }   { l  \; v^2   }   }\)

\(\large{ g = \frac   { f_d \; l \;   v^2   }   { 2 \; h_l \;  d  }   }\)

\(\large{ d = \frac   { f_d \;  l  \; v^2   }   { 2  \; h_l \;  g  }   }\)

\(\large{ l = \frac   { 2 \; h_l  \;  d  \;   g  }   { f_d \; v^2   }   }\)

 

Tags: Equations for Flow Equations for Pipe Equations for Head Equations for Hazen-Williams